Step |
Hyp |
Ref |
Expression |
1 |
|
qusgrp.h |
|
2 |
|
qusinv.v |
|
3 |
|
qussub.p |
|
4 |
|
qussub.a |
|
5 |
|
eqid |
|
6 |
1 2 5
|
quseccl |
|
7 |
6
|
3adant3 |
|
8 |
1 2 5
|
quseccl |
|
9 |
|
eqid |
|
10 |
|
eqid |
|
11 |
5 9 10 4
|
grpsubval |
|
12 |
7 8 11
|
3imp3i2an |
|
13 |
|
eqid |
|
14 |
1 2 13 10
|
qusinv |
|
15 |
14
|
3adant2 |
|
16 |
15
|
oveq2d |
|
17 |
|
nsgsubg |
|
18 |
|
subgrcl |
|
19 |
17 18
|
syl |
|
20 |
2 13
|
grpinvcl |
|
21 |
19 20
|
sylan |
|
22 |
21
|
3adant2 |
|
23 |
|
eqid |
|
24 |
1 2 23 9
|
qusadd |
|
25 |
22 24
|
syld3an3 |
|
26 |
2 23 13 3
|
grpsubval |
|
27 |
26
|
3adant1 |
|
28 |
27
|
eceq1d |
|
29 |
25 28
|
eqtr4d |
|
30 |
12 16 29
|
3eqtrd |
|